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Math Help - surjective

  1. #1
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    surjective

    Can a linear mapping ever be surjective? I can't come up with an example.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: surjective

    What about:
    f:  \mathbb{R} \to \mathbb{R}: x\mapsto x
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Re: surjective

    Quote Originally Posted by aaaa202 View Post
    Can a linear mapping ever be surjective? I can't come up with an example.
    Linear transformations are matrices, and a matrix is invertible if and only if it is square with non-zero determinant. That is, matrices with non-zero determinant are bijective linear transformations. So every invertible matrix corresponds to a surjective linear map.

    (...for a suitable value of are...)

    If you want, you could try and use matrices to classify all surjective linear maps. It is a good exercise, methinks.
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